Seismic metasurfaces on porous layered media
by Xingbo Pu
Seismic metamaterials have recently emerged as an alternative isolation strategy for the mitigation of seismic and anthropic induced vibrations. In particular, an array of sub-wavelength resonant structures located at the free surface of the soil, generally known as “seismic metasurface”, has the capabilities of impeding the propagation of surface waves by redirecting their propagation in the soil as shear waves. This phenomenon, observed numerically and experimentally in both artificially made (i.e., wave barriers and densely built environments) and natural (forest of trees) resonant systems, has motivated the derivation of ad-hoc analytical models able to predict and interpret their dynamics. Nonetheless, the even most updated models describe the metasurface substrate as a single-phase elastic medium, discarding the intrinsic heterogeneity that characterizes real soils. Such heterogeneity, which may consist in the presence of horizontal layers and water, can significantly alter the propagation of bulk and surface waves. Hence, it is important to include some of these additional complexities to correctly predict the surface wave-resonator dynamics.
For such purpose, in this work, we propose and validate an analytical model for the dispersion analysis of “metasurfaces” placed over a heterogeneous medium comprising a dry layer coupled to a saturated porous half-space. The model combines classical elasticity theory, Biot’s theory and an effective medium approach to properly treat the soil-metasurface coupling, accounting also for the fluid-solid interaction phenomena. The derived dispersion equation naturally includes simpler configurations such as metasurfaces atop fully dry and saturated soils. By leveraging our analytical model, we unveil the effect of some key poroelastic parameters like tortuosity, viscosity, water table level, on the metasurface dynamics. For values of tortuosity and viscosity characteristic of common soils, we have found a novel surface wave attenuation mechanism, additional to the canonical Rayleigh-to-shear wave conversion, induced by the downward propagation of slow pressure waves (P2 waves). This mechanism is supported by the fluid-solid interaction in the porous substrate. Besides, our analytical investigations, confirmed by numerical simulations, reveal how a change in the water-table level together with a variation in the dry vs. saturated layer mechanical parameters yields a more complex wavefield pattern, where the surface -to-shear wave conversion mechanism is accompanied by the propagation of higher-order surface modes channeled within the upper dry layer (as shown in the figure below).
Wave field of seismic metasurfaces vs. water table level: (a) h=5 m. (b) h=50 m.
More information is available in a recent publication:
Pu X., Palermo A., Cheng Z., Shi Z., Marzani A. Seismic metasurfaces on porous layered media: Surface resonators and fluid-solid interaction effects on the propagation of Rayleigh waves. International Journal of Engineering Science, 154,103347. https://doi.org/10.1016/j.ijengsci.2020.103347; https://zenodo.org/record/3941872#.YCFlzGgzZPa.
